Unlimited atonement

In a previous entry, I questioned the doctrine of limited atonement (the "L" in TULIP).  But after reading 1 John 2, I believe that a doctrine of unlimited atonement is explicitly clear:

My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father—Jesus Christ, the Righteous One. He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world. (1 John 2:1-2 NIV)

The question may remain, if Jesus was the atoning sacrifice for the whole world, then why is the whole world not saved?  I think this question is answered in the previous chapter:

But if we walk in the light, as he is in the light, we have fellowship with one another, and the blood of Jesus, his Son, purifies us from all sin.  If we claim to be without sin, we deceive ourselves and the truth is not in us. If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness. (1 John 1:7-9 NIV)

It seems to me that while atonement has been accomplished for all, justification is conditional: if you believe, confess, and walk in the Light.  This condition stated in 1 John 1 is consistent with what Paul taught in Romans 10:

If you declare with your mouth, "Jesus is Lord," and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved. As Scripture says, "Anyone who believes in him will never be put to shame."  For there is no difference between Jew and Gentile—the same Lord is Lord of all and richly blesses all who call on him, for, "Everyone who calls on the name of the Lord will be saved." (Romans 10:9-13 NIV)

Heavenly Father, thank you for the atoning work of Jesus! Thank you for atoning for the sins of the whole world! Thank you for bringing me to faith in Jesus.  Lord, please use me to lead others to understand and believe in Jesus, to confess their sin, receive His forgiveness, and walk in the Light.  I love you, and I pray in the name of Jesus.